For this case invariance under dilatation imposes that \(\Delta =\frac{d-1}{2}\) . For \(d=4\) , \(\Delta =\frac{3}{2}\) , as in the relativistic case. This matches with the previous exposition with Carrollian fermions [1]}. It is interesting to note here that even though the whole finite CCA does not turn out to be symmetries of the massive system, due to the obvious breaking of scaling invariance by the mass term, the infinite dimensional supertranslations remain a symmetry of (REF ), even with this mass term.
